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The length of the belt (Posted on 2017-05-09) Difficulty: 3 of 5
A thin belt is stretched around three pulleys, each of which is 2 feet in diameter.
The distances between the centers of the pulleys are 6 feet, 9 feet, and 13 feet.

How long is the belt?

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Raising the difficulty to 3. | Comment 4 of 5 |
The simple solution 28+2pi assumes we simply wrap the belt around the outsides of the pulleys.  This will make them all turn in the same direction.  If we want one of them to turn the other way from the others we can add a half-twist to the belt before slipping it over one of the pulleys..  

There are three ways to do this.  Say we want the pulley that is distances 6 and 13 from the others to turn the opposite way.  The half twist will make the belt cross itself near this pulley. 

I'll not share my computations, but they were tricky enough to make for a D3 exercise.  The total length is about 36.078 feet.

There are two other cases that can also be considered.

  Posted by Jer on 2017-05-09 14:54:04
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